J. Validashti

Abstract: Let R be a Noetherian ring and E a finitely generated R-submodule of a free module F. We introduce a multiplicity j(E) for E that generalizes the Buchsbaum-Rim multiplicity defined when E has finite colength in F as well as the j-multiplicity of Achilles-Manaresi that applies when E is an R-ideal. We use this notion to give a multiplicity based criterion for integral dependence of modules.

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